One of the popular methods of detecting \(\mbox{Ly$\alpha $}\)  haloes has been narrow-band (NB) stacking analyses, in particular at \(z\gtrsim 2\) , due to the faintness of \(\mbox{Ly$\alpha $}\)  haloes and the cosmic dimming effect [1]}, [2]}, [3]}, [4]}, [5]}. Until recently, individual detections have been limited to local galaxies, active galactic nuclei (AGNs), quasi-stellar objects (QSOs), and high-\(z\)  gravitationally lensed galaxies [6]}, [7]}, [8]}, [9]}, [10]}, [11]}. Large samples of individual \(\mbox{Ly$\alpha $}\)  haloes around high-\(z\)  star-forming galaxies have become available thanks to wide-field optical integral field units (IFUs) like the Very Large Telescope (VLT)/ Multi-Unit Spectroscopic Explorer [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]} and the Keck II telescope/ Keck Cosmic Web Imager [19]}, [20]}. For instance, [17]} found 145 \(\mbox{Ly$\alpha $}\)  haloes around MUSE Ly\(\alpha \)  emitters (LAEs) at \(z\approx 3\) –6. While the physical origins of \(\mbox{Ly$\alpha $}\)  haloes are still unclear, various scenarios have been suggested: CGM scattering for \(\mbox{Ly$\alpha $}\)  from star-forming regions [22]}, [23]}, gravitational cooling radiation [24]}, [25]}, [26]}, star formation in satellite galaxies [23]}, [28]}, fluorescence [29]}, [30]}, [31]}, [32]}, shock heating by gas outflows [33]}, major mergers [34]}, and combination of the aforementioned [29]}, [36]}, [37]}, [38]}, [39]}, [40]}. Despite intensive observations of \(\mbox{Ly$\alpha $}\)  haloes and studies on their origins, no clear correlations between \(\mbox{Ly$\alpha $}\)  halo properties and their galaxy hosts' properties have been found at high redshifts [13]}, [17]}. So far, the most remarkable correlation is that between the \(\mbox{Ly$\alpha $}\)  peak velocity shift and the width of \(\mbox{Ly$\alpha $}\)  lines both at ISM and CGM scales, which supports a \(\mbox{Ly$\alpha $}\)  halo scenario of resonant scattering in the outflowing medium [43]}, [44]}.
